A heuristic approximation algorithm of minimum dominating set based on rough set theory

Lihe Guan () and Hong Wang
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Lihe Guan: Chongqing Jiaotong University
Hong Wang: Chongqing Jiaotong University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 1, No 35, 752-769

Abstract: Abstract The minimum dominating set of graph has been widely used in many fields, but its solution is NP-hard. The complexity and approximation accuracy of existing algorithms need to be improved. In this paper, we introduce rough set theory to solve the dominating set of undirected graph. First, the adjacency matrix of undirected graph is used to establish an induced decision table, and the minimum dominating set of undirected graph is equivalent to the minimum attribute reduction of its induced decision table. Second, based on rough set theory, the significance of attributes (i.e., vertices) based on the approximate quality is defined in induced decision table, and a heuristic approximation algorithm of minimum dominating set is designed by using the significance of attributes (i.e., vertices) as heuristic information. This algorithm uses forward and backward search mechanism, which not only ensures to find a minimal dominating set, but also improves the approximation accuracy of minimum dominating set. In addition, a cumulative strategy is used to calculate the positive region of induced decision table, which effectively reduces the computational complexity. Finally, the experimental results on public datasets show that our algorithm has obvious advantages in running time and approximation accuracy of the minimum dominating set.

Keywords: Graph theory; Minimum dominating set; Rough set; Heuristic algorithm (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00834-x

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